Hannah Bonser, 26, stabbed Casey-Lyanne Kearney in a random attack in Elmfield Park, Doncaster, South Yorkshire, on Valentine's Day.
A jury at Sheffield Crown Court rejected Bonser's claim that she was guilty only of manslaughter due to diminished responsibility.
The judge, Mr Justice Cranston, passed the life sentence after Bonser showed no emotion as the jury foreman returned the guilty verdict following two hours of deliberation.
Sentencing her, the judge said: "Why did Hannah Bonser do this to Casey - a young girl, a complete and wholly innocent stranger?"
She sat in the dock looking ahead, as she has done throughout the week-long trial, surrounded by four prison officers.
There were cries of "Yes" from the public gallery, which was packed with Casey's family.
Her father, Anthony Kerney, appeared to wipe away tears. Many in the gallery were wearing orange ties and scarves - one of Casey's favourite colours - in memory of the teenager.
Speaking outside court, Mr Kearney said: "We think the jury has come to the correct decision in convicting Bonser with the murder of Casey.
"There was never a doubt in our minds this was a calculated and deliberate act and therefore deserves the maximum sentence our judicial system allows.
"However, no sentence will bring Casey back to us and the severity of Bonser's actions mean we will never have the privilege of her in our lives again."
Bonser, of Cusworth House, Doncaster, had denied murder.
She has a history of mental health problems and her defence team claimed she is a paranoid schizophrenic.
Her barrister, David Fish QC, had asked the jury of seven women and three men to find his client guilty of manslaughter due to diminished responsibility or lack of intent.
But prosecutors argued that she suffers from a personality disorder, not a psychosis, and was guilty of murder. The jury agreed.